A220932 - OEIS

%I #9 Mar 13 2018 16:33:46

%S 2,16,92,556,3332,19996,119972,719836,4319012,25914076,155484452,

%T 932906716,5597440292,33584641756,201507850532,1209047103196,

%U 7254282619172,43525695715036,261154174290212,1566925045741276

%N Equals two maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 n X 3 array.

%C Column 3 of A220935.

%H R. H. Hardin, <a href="/A220932/b220932.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) + 6*a(n-2).

%F Conjectures from _Colin Barker_, Mar 13 2018: (Start)

%F G.f.: 2*x*(1 + 3*x) / ((1 + x)*(1 - 6*x)).

%F a(n) = (2^n*3^(n+1) + 4) / 7 for n even.

%F a(n) = (2^n*3^(n+1) - 4) / 7 for n odd

%F (End)

%e Some solutions for n=3:

%e ..0..1..0....0..1..1....0..1..0....0..0..0....0..0..0....0..1..0....0..0..0

%e ..0..0..1....1..0..1....0..1..0....1..0..1....0..0..1....0..0..0....0..1..0

%e ..1..1..0....1..0..0....0..1..0....1..0..0....0..1..0....1..1..0....1..0..0

%Y Cf. A220935.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 25 2012